#!/usr/bin/python
# -*- coding: UTF-8 -*-
import matplotlib.pyplot as plot
import numpy as np
from matplotlib.patches import Polygon

def func(x):
    return -(x-2)*(x-8)+40

x=np.linspace(0,10)
y=func(x)
fig,ax=plot.subplots()


plot.plot(x,y,"r",linewidth=2)
a=2
b=9
ax.set_xticks([a,b])
ax.set_yticks([])
ax.set_xticklabels(["$a$","$b$"])

#画一个多边形
ix=np.linspace(a,b)
iy=func(ix)
ixy=zip(ix,iy)
verts=[(a,0)]+list(ixy)+[(b,0)]
poly=Polygon(verts,facecolor="0.8",edgecolor="0.5")
ax.add_patch(poly)

x_math=(a+b)*0.5
y_math=35
plot.text(x_math,y_math,r"$\int_a^b (-(x-2)*(x-8)+40)dx$",fontsize=10,horizontalalignment="center")

plot.figtext(0.9,0.05,"$y$")
plot.figtext(0.1,0.9,"$x$")

plot.show()